Vesselin Petkov

Relativity and the dimensionality of the world

Preface 1. The Meaning of Dimensions Paul Wesson. 2. Some Remarks on the Space-Times of Newton and Einstein Graham Hall. 3. The adventures of Spacetime Orfeu Bertolami. 4. Physics in the Real Universe: Time and Spacetime George F. R. Ellis. 5. The Real World and Spacetime Hans C. Ohanian. 6. Four-dimensional Reality and Determinism: an Answer to Stein Wim Rietdijk. 7. Relativity, Dimensionality, and Existence Vesselin Petkov. 8. Canonical Relativity and the Dimensionality of the World Martin Bojowald. 9. Relativity theory does not imply that the future already exists: a counterexample Rafael D. Sorkin. 10. Absolute Being versus Relative Becoming Joy Christian. 11. An Argument for 4D Blockworld from a Geometric Interpretation of Non-relativistic Quantum Mechanics Michael Silberstein, W.M. Stuckey, and Michael Cifone. 12. Spacetime: Arena or Reality? H. I. Arcos and J. G. Pereira. 13. Dynamical emergence of instantaneous 3-spaces in a class of models of general relativity Luca Lusanna and Massimo Pauri. 14. Lorentzian spacetimes from Parabolic and Elliptic systems of PDEs Carlos Barcelo.

Minkowski spacetime : a hundred years later

Preface Hermann Minkowski: Space and Time (English translation by Dennis Lehmkuhl) Hermann Minkowski: Raum und Zeit (original German text) PART I: The Impact of Minkowski Spacetime on the Twentieth Century Physics from a Historical Perspective Hermann Minkowski, Relativity and the Axiomatic Approach to Physics Leo Corry, Cohn Institute for History and Philosophy of Science, Tel-Aviv University Minkowskis Modern World Scott Walter, University of Nancy and H. Poincare Archives PART II: Implications of Minkowski Spacetime for Theoretical Physics Hermann Minkowski and Special Relativity Graham Hall, Department of Mathematical Sciences, University of Aberdeen The Rich Structure of Minkowski Space Domenico Giulini, Institute of Physics, University of Freiburg Minkowski Spacetime and Quantum Mechanics William G. Unruh, Department of Physics & Astronomy, University of British Columbia Modern Spacetime and Undecidability Rodolfo Gambini, Institute of Physics, Montevideo University, and Jorge Pullin, Department of Physics, Louisiana State University Quantum Spacetimes: Beyond the Continuum of Minkowski and Einstein Abhay Ashtekar, Department of Physics, Pennsylvania State University Spacetime Extensions in Quantum Gravity Martin Bojowald, Institute for Gravitational Physics and Geometry, The Pennsylvania State University PART III: Conceptual and Philosophical Issues of Minkowski Spacetime The Adolescence of Relativity: Einstein, Minkowski, and the Philosophy of Space and Time Dennis Dieks, Department of History and Foundations of Science, Utrecht University Hermann Minkowski: From Geometry of Numbers to Physical Geometry Yvon Gauthier, Department of Philosophy, University of Montreal The Mystical Formula and the Mystery of Khronos Orfeu Bertolami, Dpto. Fisica, Instituto Superior Tecnico, Lisbon, Portugal Physical Laws and Worldlines in Minkowski Spacetime Vesselin Petkov, Science College, Concordia University Time as an Illusion Paul S. Wesson, Department of Physics and Astronomy, University of Waterloo Consequences of Minkowskis Unification of Space and Time for a Philosophy of Nature Herbert Pietschmann, Institute for Theoretical Physics at the University of Vienna

On the Reality of Minkowski Space

Abstract Should physicists deal with the question of the reality of Minkowski space (or any relativistic spacetime)? It is argued that they should since this is a question about the dimensionality of the world at the macroscopic level and it is physics that should answer it.

Relativity, Dimensionality, and Existence

The main purpose of this paper is to demonstrate that the analysis of the kinematical effects of special relativity holds the key to answering the question of the dimensionality of the world. It is shown that these effects and the experiments which confirmed them would be impossible if the world were three-dimensional. Section 2 shows that relativity of simultaneity, conventionality of simultaneity, and the existence of accelerated observers in special relativity would be impossible if the world were three-dimensional. Section 3 deals with the dimensionality of physical objects and demonstrates that the relativistic length contraction and the twin paradox would be impossible if the physical bodies involved in these relativistic effects were three-dimensional objects.

Propulsion through electromagnetic self-sustained acceleration

As is known the repulsion of the volume elements of an uniformly accelerating charge or a charge supported in an uniform gravitational field accounts for the electromagnetic contribution to the charges inertial and gravitational mass, respectively. This means that the mutual repulsion of the volume elements of the charge produces the resistance to its accelerated motion. Conversely, the effect of electromagnetic attraction of opposite charges enhances the accelerated motion of the charges provided that they have been initially uniformly accelerated or supported in an uniform gravitational field. The significance of this effect is that it constitutes a possibility of altering inertia and gravitation.

Propagation of Light in Non-Inertial Reference Frames

It is shown that the complete description of the propagation of light in a gravitational field and in non-inertial reference frames in general requires an average coordinate and an average proper velocity of light. The need for an average coordinate velocity of light in non-inertial frames is demonstrated by considering the propagation of two vertical light rays in the Einstein elevator (in addition to the horizontal ray originally discussed by Einstein). As an average proper velocity of light is implicitly used in the Shapiro time delay (as shown in the Appendix) it is explicitly derived and it is shown that for a round trip of a light signal between two points in a gravitational field the Shapiro time delay not only depends on which point it is measured at, but in the case of a parallel gravitational field it is not always a delay effect. The propagation of light in rotating frames (the Sagnac effect) is also discussed and an expression for the coordinate velocity of light is derived. The use of this coordinate velocity naturally explains why an observer on a rotating disk finds that two light signals emitted from a point on the rim of the disk and propagating in opposite directions along the rim do not arrive simultaneously at the same point.

Chapter 11: Is There an Alternative to the Block Universe View?

Abstract This paper pursues two aims. First, to show that the block universe view, regarding the universe as a timelessly existing four-dimensional world, is the only one that is consistent with special relativity. Second, to argue that special relativity alone can resolve the debate on whether the world is three-dimensional or four-dimensional. The argument advanced in the paper is that if the world were three-dimensional the kinematic consequences of special relativity and more importantly the experiments confirming them would be impossible.

On the possibility of a propulsion drive creation through a local manipulation of spacetime geometry

Since the shape of a free bodys worldline is determined by the geometry of spacetime a local change of spacetime geometry will affect a bodys worldline, i.e. a bodys state of motion. The exploration of this possibility constitutes a radically new approach to the idea of how a body can be propelled: instead of applying a force to the body itself, the geometry of spacetime is subjected to a local manipulation which in turn results in the bodys motion.

Physical Laws and Worldlines in Minkowski Spacetime

In his paper “Space and Time” a hundred years ago Minkowski gave us the adequate relativistic picture of the world. According to him what exists is an absolute four-dimensional world in which the ordinary physical bodies are worldlines. Minkowski conjectured that physical laws might find their most perfect expression as interrelations between these worldlines. The purpose of this paper is to examine further whether Minkowski’s idea can be applied to different areas of physics. It is shown that not only does it work perfectly in classical physics and general relativity, but also provides a deeper understanding of some difficult questions (including the origin of inertia) and demonstrates that taking seriously the existence of worldlines inescapably leads to the concept of gravity as curvature of spacetime. It is also shown that expanding Minkowski’s idea to quantum physics might shed light even on the nature of the quantum object.

Spacetime and Reality: Facing the Ultimate Judge

Over a 100 years ago in his paper Space and Time Hermann Minkowski revealed the profound physical meaning of the relativity postulate—the experimental fact that physical phenomena are the same in all inertial reference frames implies that every inertial frame has its own space and time, which in turn implies that the Universe is an absolute four-dimensional world in which all moments of time have equal existence due to their belonging to the fourth (time) dimension. Since then there has been no consensus on the reality of this absolute world, which we now call Minkowski spacetime or simply spacetime. One might be tempted to interpret this situation in a sense that the question of the dimensionality of the world is so deep that we seem unable to comprehend it fully, which might be a manifestation of the first hints that there might exist some limits of our understanding of the world. I will argue that human abilities to understand the physical world are much greater than what most think by examining the issue of the reality of spacetime and showing that none of the experiments which confirmed the kinematic relativistic effects would be possible if the world were not four-dimensional. Therefore, facing the ultimate judge—the experimental evidence—allows us (i) to realize fully that in 1908 Minkowski had a better (than the present) understanding of the profound physical meaning of Einstein’s special relativity as a theory of an absolute four-dimensional world, and (ii) to settle the issue of the reality of spacetime once and for all.